A Bayes Analysis of Random Walk Model Under Different Error Assumptions

Abstract

In this paper, the Bayesian analyses for the random walk models have been performed under the assumptions of normal distribution, log-normal distribution and the stochastic volatility model, for the error component, one by one. For the various parameters, in each model, some suitable choices of informative and non-informative priors have been made and the posterior distributions are calculated. For the first two choices of error distribution, the posterior samples are easily obtained by using the gamma generating routine in R software. For a random walk model, having stochastic volatility error, the Gibbs sampling with intermediate independent Metropolis–Hastings steps is employed to obtain the desired posterior samples. The whole procedure is numerically illustrated through a real data set of crude oil prices from April 2014 to March 2022. The models are, then, compared on the basis of their accuracies in forecasting the true values. Among the other choices, the random walk model with stochastic volatile errors outperformed for the data in hand.